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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>(Superposition Principle)If <span class="process-math">\(u_1\text{,}\)</span> <span class="process-math">\(u_2\text{,}\)</span> <span class="process-math">\(\cdots\text{,}\)</span> <span class="process-math">\(u_k\)</span> are solutions of a homogeneous linear partial differential equation,</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
\qquad \mathcal{L}(u)=0\qquad\text{{(H)}}
\end{equation*}
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<p class="continuation">then the linear combination</p>
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\begin{equation*}
u=c_1u_1+c_2u_2+\cdots+c_ku_k,
\end{equation*}
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<p class="continuation">where <span class="process-math">\(c_i\text{,}\)</span> <span class="process-math">\(i=1,2,\cdots,k\)</span> are constants, is also a solution.</p>
<span class="incontext"><a href="sec7_6.html#p-396" class="internal">in-context</a></span>
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